$\dfrac{ -4r + s }{ -9 } = \dfrac{ -2r + 9t }{ -2 }$ Solve for $r$.
Solution: Multiply both sides by the left denominator. $\dfrac{ -4r + s }{ -{9} } = \dfrac{ -2r + 9t }{ -2 }$ $-{9} \cdot \dfrac{ -4r + s }{ -{9} } = -{9} \cdot \dfrac{ -2r + 9t }{ -2 }$ $-4r + s = -{9} \cdot \dfrac { -2r + 9t }{ -2 }$ Multiply both sides by the right denominator. $-4r + s = -9 \cdot \dfrac{ -2r + 9t }{ -{2} }$ $-{2} \cdot \left( -4r + s \right) = -{2} \cdot -9 \cdot \dfrac{ -2r + 9t }{ -{2} }$ $-{2} \cdot \left( -4r + s \right) = -9 \cdot \left( -2r + 9t \right)$ Distribute both sides $-{2} \cdot \left( -4r + s \right) = -{9} \cdot \left( -2r + 9t \right)$ ${8}r - {2}s = {18}r - {81}t$ Combine $r$ terms on the left. ${8r} - 2s = {18r} - 81t$ $-{10r} - 2s = -81t$ Move the $s$ term to the right. $-10r - {2s} = -81t$ $-10r = -81t + {2s}$ Isolate $r$ by dividing both sides by its coefficient. $-{10}r = -81t + 2s$ $r = \dfrac{ -81t + 2s }{ -{10} }$ Swap signs so the denominator isn't negative. $r = \dfrac{ {81}t - {2}s }{ {10} }$